We revisit the golfer's curse, which is the possibility that a golf ball can emerge from the cylindrical hole into which it has entered. Our analysis focuses on three constants of the motion. One of these is the energy, because we assume that the ball rolls without slipping on the inner wall of the hole, losing only a small amount of energy to rolling resistance; the other two are related to the angular momentum about the contact point of the ball with the inner wall of the hole. We develop an analysis of the motion of the ball and report measurements of the moment of inertia of a real golf ball. Solving the equation of motion along the vertical direction, we address the question of whether or not the ball could complete a vertical oscillation without reaching the bottom of the hole. We also present measurements of the dynamical friction for a golf ball and discuss dissipation in slip conditions. We conclude by proposing a challenge to golf players: to find a way to send a ball into a hole in order to make it emerge.

1.
We could not find any online videos showing such an effect in a real golf game. The best we found is a video of a putt by Tiger Woods in the 2007 PGA Championship, where the ball entered the hole only slightly, made contact with its internal surface, and then emerged after an almost 180° turn (see <https://sports.yahoo.com/blogs/golf-devil-ball-golf/look-back-tiger-woods-putt-2007-pga-championship-213256799.html>, at time 1:10). Strictly speaking, this is not completely similar to the periodic vertical motion analysed here and in the references but is similar in that the ball seemed to fall before initiating a sudden upward motion and exiting the hole.
2.
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Wolstenholme
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4.
The motion can be solved using analytical mechanics (Ref. 5). It is worth mentioning Littlewood's comment that “Golfers are not so unlucky as they think” (Ref. 6).
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Neĭmark
and
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M.
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and
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Pérez
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Holmes
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11.
In the present work, it is assumed that $Ωρ(0)$ and Ωz are unrelated quantities. They might be related under two conditions: (1) if va were identified with the initial velocity $vC(0)$ (viz., the initial velocity of C of the ball just after entering the hole), and (2) if $ż(0)$ were taken to be 0. One, thus, would arrive at the conclusion that $Ωρ(0)=Ωz$; Eqs. (32) and (35) then would become $F1(Ωz)=g(rc−rb)/(Krb2)−Ωz2$ and $F2(Ωz)=Ωz2[1+2(rc−rb)/(hc−rb)]−2g(rc−rb)2/[K(hc−rb)rb2]$. It would follow that $Ωz,1=[g(rc−rb)/K]1/2/rb$ and $Ωz,2=(rc−rb)/rb {2g/K/[(hc−rb)+2(rc−rb)]}1/2$. (We consider only the positive values of $Ωz.$) With the values of Table I, we have $Ωz,1≈43$ and $Ωz,2≈29 rad s−1$, which would correspond to approaching velocities $va,1∼rbΩz,1≈0.93$ m s−1 and $va,2∼rbΩz,2≈0.58 m s−1$, in perfect agreement with Fig. 5. Because the interaction between the hole and the ball is complex (see Ref. 10), the conditions (1) and (2) are not obvious. It is, thus, reasonable and simpler from a pedagogical point of view to consider $Ωρ(0)$ and Ωz as independent.
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Zengel
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Gutterballs and rolling down the tubes
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13.
The ball is obviously neither homogeneous nor a perfect sphere; we would expect K to be different from 2/5 and 2/3. However, the experimental study gave a value close to 0.4 (cf. 4.1).
14.
Consider a mobile point M (position $rM$, velocity $vM=drM/dt)$ in the time derivative of the angular momentum; O is the origin of the lab frame, viz., a fixed point in this frame. Since $LM=LO−rM×P$, where $P=mvC$ is the total linear momentum, we have, when taking the time derivative of $LM$, $dLM/dt=dLO/dt−vM×P−rM×dP/dt$. Moreover, the torque about M of all the forces $(F=dP/dt)$ is $ΓM=ΓO−rM×F$. Because $dLO/dt=ΓO$, we obtain for the angular momentum theorem about a mobile point $dLM/dt+vM×P=ΓM$. This explains the term $mvI×vC$ in Eq. (8).
15.
We did not manage to find exactly the first equation in this examination. Specifically, we do not find the constant term $17g sin α/b$; the 17 is mysterious. Also, to be consistent with the two other equations, it seems that $(dϕ/dt)2$ may correspond to $Ωe2−Ωe(0)2$. If α = 0, then $(dϕ/dt)2=0$ and $Ωe=Ωe(0)=constant$, as in the present work (Eqs. (3) and (11)).
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and
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P.
Appell
and
S.
Dautheville
,
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(
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23.
See <https://en.wikipedia.org/wiki/Rolling_resistance> for information about the factor of rolling friction, in particular the Section Physical formulae, and the numerous references therein (in this webpage).